Just as you may have been told to grow basil with your tomatoes for them to grow better, or marigolds to repel pests... These are not old wives' tales, studies have confirmed both and many other productive plant pairings.
Anglianhome.co.uk's "A Vegetable Growing Cheat Sheet" (portion on the right, go to link for full chart) makes the whole thing very simple. But is limited to the most common / popular vegetables in the UK.
Wikipedia's List of Companion Plants not only lists those that help, but also those that might harm the yield of certain vegetables and fruit trees (e.g. beets and bush beans don't get along). Reading the entire list and trying to incorporate everything, however, is a little like planning a wedding seating chart for friends, feuding family members, and fawning couples (with some history of the relationships)... But if one can get similar results as 20% more tomatoes when grown with basil with other vegetables, it seems worth it to doing a little investigating.
AfriStar Foundations "Companion Plantings" (below) is a great balance of the two - not too detailed, not too simplified. The names of the plants might be a little different from what we're used to, but there are pictures to help.
For more information about different plant pairings not just for the vegetable garden also see Organic Gardening's Beginner's Guide to Companion Planting.
Bee-Friendly: Companion planting encourages not using pesticides, instead working with nature by attracting beneficial bugs, repelling pests, or luring pests away.